Abstract : Research has been conducted to advance the state of the art in (a) multiple scale modeling of advanced heterogeneous materials, (b) in large deformation analysis of solids with applications in metal forming, and also (c) in solidification modeling. For modeling heterogeneous materials (a), a new Voronoi Cell finite element model has been developed which naturally evolves from the microstructure. Formulations have been developed for thermo-dasticity, elasto-plasticity and heat conduction. This is then cast in multiple scale modeling of heterogeneous (porous and composite) materials by combining with asymptotic homogenization theory. In (b), an adaptive arbitrary Lagrangian-Eulerian (ALE) finite element method has been developed for solving metal forming problems with strain localization. The ALE mesh movement is coupled with r-adaptation to minimize element distortion, and with s-adaptation to achieve local enrichment. Finally heat transfer analysis for solidification problems has been conducted to evaluate the temperature field and location of the phase change interface using the ALE description. (AN)